Some new formulas for π

被引：11
|
作者：
Almkvist, G [1 ]
Krattenthaler, C
Petersson, J
机构：
[1] Lund Univ, Inst Matemat, SE-22100 Lund, Sweden
[2] Univ Lyon 1, Inst Girard Desargues, F-69622 Villeurbanne, France
来源：
EXPERIMENTAL MATHEMATICS | 2003年 / 12卷 / 04期
关键词：
Fast converging series for pi; determinant evaluations;
D O I：
10.1080/10586458.2003.10504512
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show how to find series expansions for pi of the form pi = Sigma(n=0)(infinity) S(n)/((mn)(pn)) a(n), is some polynomial in n (depending on m,p,a). We prove that there exist such expansions for m = 8k, p = 4k, a = (-4)(k), for any k, and give explicit examples for such expansions for small values of m, p and a.
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页码：441 / 456
页数：16
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